This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoff’s classical theory on analytic difference equations on the other.
Produkteigenschaften
- Artikelnummer: 9784431539124
- Medium: Buch
- ISBN: 978-4-431-53912-4
- Verlag: Springer Japan
- Erscheinungstermin: 13.05.2011
- Sprache(n): Englisch
- Auflage: 2011
- Serie: Springer Monographs in Mathematics
- Produktform: Gebunden, HC runder Rücken kaschiert
- Gewicht: 670 g
- Seiten: 320
- Format (B x H x T): 160 x 241 x 23 mm
- Ausgabetyp: Kein, Unbekannt